InterviewSolution
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InterviewSolution
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If `a=(3+sqrt5)/2` then find the vaule of `a^(2)+1/(a^(2))` |
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Answer» `given , a=(3+sqrt5)/2` `1/a=2/(3+sqrt5)=2/(3+sqrt5)xx(3-sqrt5)/(3-sqrt5)` [multiplying numerator and denominator by `3-sqrt5`) `(6-2sqrt5)/(3^(2)-(sqrt5)^(2)) " " ["using identity" , (a-b)(a+b)=a^(2)-b^(2)]` `(6-2sqrt5)/(9-5)=(6-2sqrt5)/4` `1/a=(2(3-sqrt5))/4=(3-sqrt5)/2` `a^(2)+1/(a^(2))a^(2)+1/a^(2)+2-2=(a+1/a)^(2)-2" " ["adding and subtarcting2"]` `((3+sqrt5)/2+(3-sqrt5)/2)^(2)-2 " " ["from Eqs. (i)and (ii)"]` `(6/2)^(2)-2=(3)^(2)-2=9-2=7` |
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